SIGNIFICANT FIGURES

1
SIGNIFICANT FIGURES
In measurement the number of significant figures
(SF) is an indication of the precision of the
recorded measurement. Examples 2 SF - 24
2.4 0.24 0.0024 0.020 3 SF - 364 36.4
0.000364 0.0240 4 SF -
7621 76.21 0.0007621 24.00 SF is not equal to
the number of decimal points SF RULES IN ADDING
AND SUBTRACTION Round off to the rightmost column
containing a significant figure Example 4 6 .
4 3 0 2 1 . 0 2 3 7
5 . 0 0 . 0 0 0 2
--------------------------
4 2 2 . 4 5 0 4 4 2 2 . 5 (rounded)
See http//www.scimedia.com/chem-ed/data/sig-figs.
htm
2
SF RULES FOR MULTIPLICATION AND DIVISION
The number of digits in the final answer should
equal the least number of significant figures in
any of the factors Example 3.50 6.3 /
7.1275 3.09365 3.1 (rounded)

• SPECIAL CASES IN GEOMATICS
• Intermediate calculations should carry one more
  digit than required to prevent round-off errors
• There may be an implied number of SF, e.g.
  football field of 100 yards would actually be
  measured to the nearest hundredth of a foot
• Different factors cause different variations,
  e.g. a change in temperature of 15F changes the
  length of a100.00ft steel tape by only 0.01ft,
  therefore working to 5 SF is justifiable
• When converting between units of measure, the
  conversion factor may be exact, e.g. 1 m
  39.37 in (Survey foot)

3

• ROUNDING OFF RULES
• When last digit after SF is gt 5
  increase last digit by 1
• e.g. 10.678 becomes 10.68
• When last digit after SF is lt 5 drop last
  digit
• e.g. 10.673 becomes 10.67
• When last digit after SF is 5 round to
  nearest even number
• e.g. 10.675 becomes 10.68

UNUSUAL CASES e.g. 4200 - unclear whether 2
SF or 4 SF to clarify write as 42 x 102 if
2 SF e.g. 10.675000001 last digit after SF is
gt5 therefore round to 10.68
4
Example

• Convert the distance 3273.027m to Int. Feet
• 3273.0273.280839895 10738.28 Int Ft
• (7 Sig Figs of the distance dictates the rounding
  off of the answer)
• Convert the distance 3273.027m to Survey Feet
• 3273.0273.2808333333 10738.26 Survey Ft